White blood cell population dynamics

ABSTRACT

Systems and methods for modeling and detecting white blood cell population dynamic for diagnosis and treatment, e.g., of acute coronary syndrome or leukocytosis.

CLAIM OF PRIORITY

This application is a divisional of U.S. patent application Ser. No.16/091,576, filed Oct. 5, 2018, which is a § 371 National StageApplication of PCT/US2017/026695, filed on Apr. 7, 2017, which claimsthe benefit of U.S. Provisional Application Ser. No. 62/319,370, filedon Apr. 7, 2016, U.S. Provisional Application Ser. No. 62/437,468 filedon Dec. 21, 2016, and U.S. Provisional Application Ser. No. 62/466,590filed on Mar. 3, 2017. The entire contents of the foregoing areincorporated herein by reference.

FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

This invention was made with Government support under Grant No. DK098087awarded by the National Institutes of Health. The Government has certainrights in the invention.

TECHNICAL FIELD

Described herein are systems and methods for modeling and detectingwhite blood cell population dynamic for diagnosis and treatment, e.g.,of acute coronary syndrome or leukocytosis.

BACKGROUND

Circulating blood cells continuously interrogate almost all tissues inhigh throughput, and their collective states of maturation, activation,and proliferation reflect current pathophysiologic states, includinghealthy quiescence, acute response to pathology, chronic compensationfor disease, and ultimately de-compensation. The complete blood count(CBC) reflects these pathophysiologic states. An elevated white bloodcell count (WBC) may reflect an ongoing response to infection,hematologic malignancy, or other inflammatory process. The WBCdifferential reports the fraction of each sub-type of WBC, principallyneutrophils, lymphocytes, and monocytes. Patients with high WBC countsmay be further classified depending on the predominant WBC subtype forappropriate additional diagnostic testing and patient assessment¹⁻³.

SUMMARY

Routine complete blood counts (CBC) provide estimates of numbers ofcurrently circulating white blood cells (WBC) and platelets. CBCs alsoprovide current average values for a number of single-WBC andsingle-platelet characteristics including morphology (e.g., volume) andsurface markers (e.g., CD4). WBC counts and platelet counts areimportant in the diagnosis and management of a wide range of diseases.Current average values of single-WBC and single-platelet characteristics(for instance, neutrophil volume and mean platelet volume) have alsobeen found to correlate strongly with a number of diseases. Anunderstanding of the rates and directions of change in these counts andcharacteristics would provide earlier and more accurate diagnosis formany conditions.

Provided herein are methods that include receiving data indicative of aproperty value of each white blood cell (WBC) in a sample of white bloodcells (WBCs) of a patient, wherein the data comprises single-cellmeasurements from a complete blood count; and determining, usingparameter estimation, a value indicative of WBC population dynamics ofthe patient based on the data indicative of the property value of eachWBC.

In some embodiments, the data comprises optical, fluorescence, orimpedance single-cell measurements from a complete blood count.

In some embodiments, the data is indicative of a morphological propertyor intracellular composition of each WBC in the sample.

In some embodiments, the data is indicative of cell size, internalcomplexity, nuclear lobularity, peroxidase content, or DNA/RNA contentof each WBC in the sample.

In some embodiments, the data comprise one or more of Axial Light Loss(ALL) representing cell size; Intermediate Angle Scatter (IAS)representing cellular complexity; Polarized Side Scatter (PSS)representing nuclear lobularity; Depolarized Side Scatter (DSS)distinguishing granulocytes (neutrophils and eosinophils); and afluorescence signal separating nucleated red blood cells, stromal cellsand the mononuclear agranulocytes (lymphocytes and monocytes).

In some embodiments, the data are used to determine one or more valuesselected from the group consisting of α_(ALL), D_(ALL), α_(IAS),D_(IAS), K_(PSS), α_(SSC,L), α_(SSC,M), α_(RNA/DNA,L), D_(SSC,L),D_(SSC,M), and D_(RBA/DNA,L).

In some embodiments, the methods include the one or more values to areference value. In some embodiments, the reference value represents anidentified cohort of subjects, or a value determined at an earlier orlater point in time in the same subject.

In some embodiments, the WBCs are selected from the group consisting ofneutrophils, lymphocytes, and monocytes.

In some embodiments, the methods include receiving data indicative of acomplete blood count of the patient, wherein receiving the dataindicative of the complete blood count comprises receiving the dataindicative of the property value of each WBC.

In some embodiments, the property value of the parameter is estimatedbased on data indicative of a predefined normalized property value ofWBCs.

In some embodiments, the methods include receiving data indicative of afirst complete blood count of the patient in which the property value ofeach WBC in a first sample of WBCs is measured, and receiving dataindicative of a second complete blood count of the patient in which theproperty value of each WBC in a second sample of WBCs is measured,wherein the value of the parameter is estimated based on the dataindicative of the first complete blood count and the data indicative ofthe second complete blood count.

In some embodiments, the methods include receiving data indicative of anormal template or ensemble of normal complete blood counts in which theproperty value of each WBC in a first sample of WBCs is measured, andreceiving data indicative of a second complete blood count from thepatient in which the property value of each WBC in a second sample ofWBCs is measured, wherein the value of the parameter is estimated basedon the data indicative of the first complete blood count and the dataindicative of the second complete blood count.

In some embodiments, the property value is indicative of a property ofeach WBC selected from the group consisting of cell size, cytoplasmicgranularity, morphology, nuclear morphology, and nuclear granularity.

In some embodiments, receiving the data indicative of the property valueof each WBC comprises receiving data indicative of axial light lossmeasurements of the sample of WBCs, intermediate light loss measurementsof the sample of WBCs, or polarized side scatter measurements of thesample of WBCs.

In some embodiments, the parameter indicative of the WBC populationdynamics of the patient is indicative of a drift or a diffusion of theWBC population dynamics.

In some embodiments, the methods include providing information fortreatment or diagnosis of a condition of the patient associated with aninflammatory or immune system response based on the parameter.

In some embodiments, the condition is selected from the group consistingof a hematological malignancy, acute coronary syndrome, urinary tractinfection, and an autoimmune disease.

In some embodiments, providing information for treatment or diagnosis ofa condition of the patient associated with an inflammatory immune systemresponse based on the parameter comprises providing information fortreatment or differential diagnosis of reactive leukocytosis andmalignant leukocytosis.

In some embodiments, the troponin level of the patient is within normalrange, and or a WBC count is within normal range (e.g., 4,000-11,000cells/ul blood). The methods can include determining the troponin levelof the patient, using known methods.

Also provided herein are systems comprising a processing device, and oneor more computer-readable non-transitory media storing instructions thatare executable by the processing device, and upon execution cause theprocessing device to perform a method described herein. For example, themethods can include operations comprising: estimating a value of aparameter indicative of white blood cell (WBC) population dynamics of apatient based on data indicative of a property value of each WBC in asample of white blood cells (WBCs) of the patient, the property value ofa WBC being indicative of an age of the WBC; and optionally providinginformation for treatment or diagnosis of a condition of the patientassociated with an inflammatory or immune system response based on theparameter.

In some embodiments, the WBCs comprise cells selected from the groupconsisting of neutrophils, lymphocytes, and monocytes.

In some embodiments, the operations include receiving data indicative ofa complete blood count of the patient, the data indicative of thecomplete blood count being indicative of the property value of each WBC.

In some embodiments, the property value of the parameter is estimatedbased on data indicative of a predefined normalized property value ofWBCs.

In some embodiments, the operations further comprise: receiving dataindicative of a first complete blood count of the patient in which theproperty value of each WBC in a first sample of WBCs is measured, andreceiving data indicative of a second complete blood count of thepatient in which the property value of each WBC in a second sample ofWBCs is measured, wherein the value of the parameter is estimated basedon the data indicative of the first complete blood count and the dataindicative of the second complete blood count.

In some embodiments, the operations further comprise: receiving dataindicative of a normal template or ensemble of normal complete bloodcounts in which the property value of each WBC in a first sample of WBCsis measured, and receiving data indicative of a second complete bloodcount of the patient in which the property value of each WBC in a secondsample of WBCs is measured, wherein the value of the parameter isestimated based on the data indicative of the first complete blood countand the data indicative of the second complete blood count.

In some embodiments, the property value is indicative of a property ofeach WBC selected from the group consisting of cell size, cytoplasmicgranularity, morphology, nuclear morphology, and nuclear granularity.

In some embodiments, receiving the data indicative of the property valueof each WBC comprises receiving data indicative of axial light lossmeasurements of the sample of WBCs, intermediate light loss measurementsof the sample of WBCs, or polarized side scatter measurements of thesample of WBCs.

In some embodiments, the parameter indicative of the WBC populationdynamics of the patient is indicative of a drift or a diffusion of theWBC population dynamics.

In some embodiments, the parameter is selected from the group consistingof α_(ALL), D_(ALL), α_(IAS), D_(IAS), K_(PSS), α_(SSC,L), α_(SSC,M),α_(RNA/DNA,L), D_(SSC,L), D_(SSC,M), and D_(RBA/DNA,L).

In some embodiments, the condition is selected from the group consistingof a hematological malignancy, acute coronary syndrome, urinary tractinfection, and an autoimmune disease.

In some embodiments, providing information for treatment or diagnosis ofa condition of the patient associated with an inflammatory immune systemresponse based on the parameter comprises providing information fortreatment or differential diagnosis of reactive leukocytosis andmalignant leukocytosis.

In some embodiments, a troponin level of the patient is within thenormal range (e.g., normal <0.03 ng/ml, abnormal >0.09 ng/ml, andindeterminate in between), and or a WBC count is within normal range.

Unless otherwise defined, all technical and scientific terms used hereinhave the same meaning as commonly understood by one of ordinary skill inthe art to which this invention belongs. Methods and materials aredescribed herein for use in the present invention; other, suitablemethods and materials known in the art can also be used. The materials,methods, and examples are illustrative only and not intended to belimiting. All publications, patent applications, patents, sequences,database entries, and other references mentioned herein are incorporatedby reference in their entirety. In case of conflict, the presentspecification, including definitions, will control.

Other features and advantages of the invention will be apparent from thefollowing detailed description and figures, and from the claims.

DESCRIPTION OF DRAWINGS

(FIGS. 1-9 show results with data collected on an Abbott hematologyanalyzer.)

FIGS. 1A-D. (A) Schematic showing the analytic workflow. (B) Patientspecific scatter plot showing the optical measurements, as measured bythe Abbott CELL-DYN Sapphire instrument with the intermediate-anglescatter intensity (IAS) and the axial light-loss intensity (ALL), with Bat healthy state and (C) at the time of an elevated Troponinmeasurement. (D) Probability distribution for the lymphocyte populationat the healthy and diseased state, contour plot shows how the modelcaptures the trajectory of the probability distribution for a WBCsubpopulation based on drift and diffusion, as the blood cellpopulations are perturbed or altered in response to a pathologiccondition.

FIGS. 2A-F. (A-E) Comparison of the different model parameters foracutely ill patients (Study) and healthy individuals (Control).Parameter estimation for each patient required a CBC at two differenttime points but can also be done with a normal template (e.g., a set ofreference levels determined using data from a defined cohort ofsubjects, e.g., normal/healthy or disease reference subjects) as astarting point. Study and Control patients had normal WBC counts(4,000-11,000 cells/ul) at both time points (E) This panel shows thelog-transformed p values (−log(p)) for the model parameters (subscript Lis for lymphocytes (n_(low)=123, n_(high)=141), M for monocytes(n_(low)=88, n_(high)=71), and N for neutrophils (n_(low)=62,n_(high)=64)). Points above the dashed line (−log(0.05)) aresignificant. The number of observations differs in each cohort due tothe exclusion of unsatisfactory parameter fits. These resultsdemonstrate that the model can, in general, distinguish patients withacute illnesses from those who are healthy, even when the two groups arenot distinguishable based on WBC counts alone.

FIGS. 3A-F. Comparison of the model parameters for patients who have twonormal (low) Troponin measurements versus patients whose Troponin isinitially normal and subsequently elevated. Because absolute WBC counthas already been shown to correlate with Troponin level and risk ofacute coronary syndrome (ACS), we matched WBC counts such that theydiffered by less than 500/ul at both time points in order to focus onchanges in WBC dynamics independent of absolute WBC count. Low Tn-Tgroup (Low Tn-T), Increasing Tn-T (High Tn-T) group, (A) α_(ALL), (B)D_(ALL), (C) α_(IAS), (D) D_(IAS). (E) K_(PSS) pertains to theNeutrophil population only. (F) Showing the transformed p values(−log(p)) for the model parameters (subscript L is for lymphocytes(n_(low)=143, n_(high)=183), M for monocytes (n_(low)=106,n_(high)=137), and N for neutrophils (n_(low)=115, n_(high)=137)).Points above the dashed line (−log(0.05)) are significant.

FIGS. 4A-F. Predicting which patients with normal Troponin will have anelevated Troponin at some point in the subsequent 48 hours. ROC curvesfor cross-validated decision tree classifiers using the significantmodel parameters are shown. The dashed line corresponds to an area underthe curve (AUC) of 0.5, which indicates no predictive ability of theclassifier. The parameters considered in the classifier are lymphocyteD_(ALL), α_(IAS); neutrophil α_(ALL), K_(PSS); and monocyte D_(ALL). (A)Receiver operating characteristic (ROC) curve for the decision treeclassifier developed with the training data set under five-foldcross-validation. (B) Confusion matrix showing the performance of thecross-validated decision tree on the training set. (C) ROC curve for thesame cross-validated decision tree applied to an independent validationset and showing a similar AUC as expected for cross-validation(n_(low)=50, n_(high)=50). (D) Confusion matrix showing the performanceof the cross-validated trained classifier on the validation set. (E) ROCcurve for a decision tree classifier trained for the full training dataset without cross-validation. (F) ROC curve for the non cross-validatedclassifier applied to an independent data set.

FIGS. 5A-B. (A) Comparison of WBC differentials between the cohortswhose Troponin-T goes up (High), versus those whose Troponin remainednormal (Low). LYM, Lymphocytes; MON, Monocytes; NEU, Neutrophils. Thesepatient groups cannot be distinguished based on the tradition WBCdifferential. (B) Depiction of the drift functions in the mathematicalmodel.

FIGS. 6A-C. Representation of the distribution upon parameter fittingusing the mathematical model for the lymphocyte population (Black-Fitteddistribution, White-Empirical/measured distribution). For thisparticular fitting exercise, the sum of square of errors/objectivefunction was 1.56e-4, and the first order optimality condition was1.11e-4, demonstrating a very good fit of the model to the data. (A)Surface plot showing the fitted distribution, (B) X-Z projection of thesurface plot in (A), (C) Y-Z projection of the surface plot in (A).

FIGS. 7A-C. Varying mathematical expressions chosen for the drift withrespect to the ALL grid (A) Original piecewise expression, (B) PiecewiseQuadratic, (C) Piecewise Linear. The qualitative shapes of these curvesis what makes the model informative and not the specific mathematicalexpression.

FIGS. 8A-H. (A-D) Comparing the model parameters using the differentexpressions for α_(ALL) (O-Original, L-Linear, Q-Quadratic) from FIGS.7A-C, and using Equation 5 for α_(IAS). (In each section, the left handbar depicts the original expression as shown in Equation 4, the middlebar depicts the linear expression as shown in Equation 11, and the righthand bar depicts the quadratic expression as shown in Equation 12). Theparameters for the low Tn-T cohort versus the high Tn-T cohort have beencompared separately (Low Tn-T depicted by x-axis tick label, L; HighTn-T depicted by x-axis tick label, H). (E-H) Comparing the modelparameters using the different expressions for α_(IAS), but usingEquation 4 for α_(ALL). (In each section, the left hand bar depicts theoriginal expression as shown in Equation 5, the right hand bar depictsthe linear expression as shown in Equation 13). The parameters for thelow Tn-T cohort versus the high Tn-T cohort have been comparedseparately (Low Tn-T depicted by x-axis tick label, L; High Tn-Tdepicted by x-axis tick label, H). Patient-specific model parameters aredetermined by the qualitative mechanistic structure of the equations andnot the specific mathematical expressions.

FIGS. 9A-L. Comparing the model parameters for patients with nomeasurements of Tn-T (healthy), normal (low) Tn-T, and high Tn-T for(A-D) Lymphocytes, (E-H) Neutrophils, and (I-L) Monocytes.

(FIG. 10 shows data collected on a Sysmex hematology analyzer.)

FIGS. 10A-L. Parameter estimates for cellular population dynamics oflymphocytes, monocytes, and neutrophils for patients with malignantversus reactive leukocytosis. Five (marked with *) of 12 parametersindependently provide statistically significant discrimination (p<0.05)between pilot cases (n=20) and controls (n=22). Parameter distributionsare shown as notched boxplots where the central horizontal line showsthe median, the box extends from the 25th to the 75th percentile, andthe notches show the extent of a 95% confidence interval for the median.Dashed lines show extent of outliers that are no farther from the medianthan 1.5-times the inter-quartile range. Plus symbols show more extremeoutliers.

(FIGS. 11-13 show data collected on a Siemens hematology analyzer.)

FIG. 11 . Distributions of neutrophil size and complexity for twopatients subsequently diagnosed with acute myelogenous leukemia (AML).The left panel is from a patient with very aggressive disease, the rightfrom a patient with slowly progressing disease. Aggressive disease wasassociated with greater diffusivity in the WBC population dynamics,leading to an increase in the variation (width) in neutrophil nuclearcomplexity as demonstrated by the wider contour plot in the left panelcompared to the right. The pattern was statistically significant in aset of 120 patients with newly diagnosed AML.

FIG. 12 . Surface plot of the data in FIG. 11A, with the z-axis showingthe number of cells.

FIG. 13 . Lymphocyte population dynamics for two patients with chroniclymphocytic leukemia (CLL). The left surface and contour plots show thedistributions of lymphocyte size and peroxidase content at an initial(top left) and later (bottom left) time point. This patient's diseasewas stable as were the lymphocyte population distributions (shape of thesurfaces and contours), despite a significant increase in lymphocytecount (z-axis). The right surface and contour plots show a patient withprogressing disease whose lymphocyte count increased by the samefraction. Progressive disease was associated with a qualitative changein lymphocyte population dynamics seen as a change in the shapes of thesurface and contour plots.

DETAILED DESCRIPTION

Most automated hematology analyzers are sophisticated instruments thatmeasure several single-cell characteristics for tens of thousands ofWBCs, RBCs, and platelets. Each routine CBC thus involves hundreds ofthousands of single-cell measurements, but clinical decisions areusually based on only a few derived statistics, e.g., a total count ofWBCs, RBCs, and platelets. The vast potential of the complete data setcollected during each CBC measurement has been well-appreciated, andmany previous efforts have been undertaken to extract additionalinformation, for instance by trying to detect early infection byidentifying “immature” granulocytes sometime called “band” cells, orguiding stem cell collection by estimating the number of circulatinghematopoietic progenitor cells, or providing early detection of somehematologic malignancies by counting the number of WBCs with atypicalcharacteristics. These efforts have had limited impact but hint at thepotential for clinical decision support within these large data setscollected during routine CBCs⁴. More recent work has combined theseexisting high-resolution clinical data sets with semi-mechanistic modelsof blood cell maturation, activation, and clearance to providepatient-specific estimates of the rates of these cellular processes. Thepopulation dynamics of a patient's blood cells often sensitively reflectpathophysiologic states and thus provide insight into physiologicprocesses and opportunities for earlier and more accurate diagnosis andprognosis¹².

Described herein are dynamic population models using raw CBCmeasurements for neutrophil, lymphocyte, and monocyte populations. Thedynamic population models can be used to estimate changes in the WBCcount and population over a period of time. For example, the parametersof the dynamic population models can be indicative of rates of change ofthe WBC count. While a single measurement of a WBC count accounts forthe current number of WBCs, the parameters of the dynamic populationmodels are indicative of changes in the WBC count over time and thus canbe used for early diagnosis or treatment of a patient for a condition.

The CBC can be performed on a sample of WBCs from a patient and canprovide measurements of morphological properties and intracellularcomposition (e.g. size, internal complexity, nuclear lobularity,peroxidase content, DNA/RNA content) of each WBC in the sample. Based onthe measurements of the properties of each WBC, the models quantify therates of change in these characteristics for a typical WBC as well asthe variation in the rates of change from one cell to the next and forthe same cell at different points. These rates of change in single-cellcharacteristics and the magnitude the variation in these rates of changeare associated with changes of each WBC count, e.g., a neutrophil count,a lymphocyte count, or a monocyte count. For instance, young neutrophilsare larger on average than mature neutrophils, and an increased rate ofproduction of new neutrophils is thus associated with an increase in theaverage size of a patient's circulating neutrophil population, and therate of increase in the average size thus provides an estimate of therate of increase in the neutrophil count. As another example,cytoplasmic granularity increases during infection, and the rate ofincrease can be correlated with the intensity of the inflammatoryresponse. The rates of change in the single-WBC characteristics measuredby the CBC thus enable quantification of the net effects of cellularproduction, maturation, activation, and clearance on these three WBCsubpopulations. As shown herein, these dynamics are different betweenhealthy and sick patients, even in those whose absolute WBC counts areindistinguishable. As a result, the population dynamics and the rates ofchange of morphological and compositional attributes of the populationsof WBCs can be used to differentiate healthy and sick patients, eventhose who have similar WBC counts.

To determine the rate of change of the WBC count, a property indicativeof a maturity or age of each WBC can be measured. The property can be amorphological characteristic or an optical characteristic that isindicative of an age or maturity or activation state of a WBC. Theproperty can be, for example, a cell size, a cytoplasmic granularity, amorphology, a nuclear morphology, or nuclear granularity. For a givenWBC, any of these properties can be an indicator of a current age of theWBC. In this regard, measurements of any one of these properties foreach WBC can be used to characterize dynamics of the population of theWBCs.

Model parameters can be estimated for individual patients, e.g., usingone or more routine CBCs, e.g., pairs of routine CBCs, e.g., using astandard normal template CBC and a single patient CBC. Values of themodel parameters are estimated based on the measurement of the propertyof each WBC in the sample of WBCs taken from the patient. The clinicalrelevance of these models is shown in acute coronary syndrome, one ofthe leading causes of death worldwide, and leukemia/reactiveleukocytosis. Inferring a patient's WBC population dynamics improves therisk stratification of patients being evaluated for acute coronarysyndrome or the diagnosis of reactive leukocytosis (e.g., infection)versus malignant leukocytosis (e.g., leukemia) using existing routineclinical data.

Measuring WBC Population Dynamics

Many common clinical laboratory hematology analyzers measure single-WBCand single-platelet morphologic characteristics, for instance, analyzerssold by Abbott, Sysmex, Siemens, and Beckman. These devices measuredifferent optical or morphologic characteristics of each WBC in apatient blood sample. These characteristics were selected on the basisof their ability to distinguish WBCs from different lineages and atdifferent levels of maturation and thus can be used to estimate an age,maturity, or activation state of a WBC. For instance, many analyzersinclude single-WBC optical characteristics with intensities thatcorrelate with the degree of nuclear lobularity, which, in turn, iscorrelated with the degree of maturation, e.g., the age of the WBC. See,e.g., Bainton et al., Developmental Biology of Neutrophils andEosinophils, 1969, Ser Haematology 3: 3-43.

Modeling can proceed with the raw device measurements or with themapping of those device measurements into a standard instrument-neutralset of coordinates (age=f¹(raw)) reflecting estimated age andactivation. When the raw device measurements are used, then f¹ is simplydefined as the identify function.

Given a single-cell or single-platelet characteristic, normal magnitudeof variation is quantified by analyzing distributions among a healthycohort. This variation is decomposed into components of drift anddiffusion which are included in models of single-cell andsingle-platelet population dynamics.

Dynamics for each characteristic (raw or mapped) are preferably modeledin the following way. Given a cell or platelet's position along acharacteristic coordinate (e.g., side scatter or SSC), establishedphysiologic mechanisms are used to constrain the mathematical form of anequation describing the cell's most likely position along thatcoordinate at the next point in time as a function of all availablecurrent characteristics. For characteristics whose levels increase withtime on average, the relation looks like the following.d/dt N(f ⁻¹(SSC))=αN(f ⁻¹(SSC)−1, . . . )where N( ) represents the number or proportion of cells or plateletswhose SSC value is the same at time t and whose other characteristics(e.g., forward scatter, RNA/DNA content, peroxidase content, axial lightloss, intermediate angle scatter, polarized side scatter, depolarizedside scatter, electrical impedance, etc.) are included as necessary.Second-order diffusive terms can be added where appropriate based onknown physiology or mechanistic uncertainty.

A similar expression is derived for the number or fraction of cellsproduced with the same level of SSC: γN₀(f⁻¹(SSC), . . . ). Thisexpression, when positive, contributes to a positive rate of change ofthe cell count.

A similar expression is derived for the number or fraction of cellscleared from the circulation with the same level of SSC: δN₀(f⁻¹(SSC), .. . ). This expression, when positive, contributes to a negative rate ofchange of the cell count.

These processes can be combined to yield an expected rate of change inthe number of cells or platelets with a given set of characteristics:d/dt N(f ⁻¹(SSC))=αN(f ⁻¹(SSC)−1)−βN(f ⁻¹(SSC))+γN ₀(f ⁻¹(SSC))−δN(f⁻¹(SSC))

The model parameters scaling each contributing process can then beidentified for individual patients from their raw complete blood countmeasurements. These parameters are then used to provide ahigh-resolution hematologic and immunologic phenotype which can be usedto screen patients for common illness and within chronic disease groupsto stratify patients for risk. Although the exemplary approach describedin the examples below used multiple CBC measurements from the samepatient, in other methods a reference level can be used that representsa chosen population, developed using standard statistical methods basedon a selected cohort of patients.

Parameters for population dynamics of different cell types or plateletscan be combined in composite diagnostic algorithms. For instance, whilean increasing neutrophil size or count alone increases the near-termrisk of an infection, the combination of an increasing neutrophil countor size and a decreasing lymphocyte count or size (below) may be bettercorrelated with a diagnosis of leukemia.

These methods may be used to make new diagnoses earlier and moreaccurately than is otherwise possible and may also be used to stratifypatients with chronic disease, for instance predicting prognosis for twodifferent patients with chronic lymphocytic leukemia as shown below.

Acute Coronary Syndrome

Acute coronary syndrome is caused by insufficient oxygen supply to themyocardium and involves either a myocardial infarction (MI) or unstableangina⁶. It was hypothesized that the severe ischemia and developinginfarction can trigger an immediate and substantial systemicinflammatory response that can be detected in terms of its perturbationsof the dynamics of WBCs. Troponin I, C and T (Tn-I, Tn-C, Tn-T) areproteins found in the cardiac muscles, which start leaking and becomedetectable in the blood, upon necrosis of these cardiac tissues⁷⁻⁹.Serum levels of this protein typically increase over a few hours, andpeak over several hours and up to a day or two, from the onset ofsymptoms and are currently the current gold standard for diagnosing MI.In contrast, patients experiencing unstable angina or other pathologynot associated with MI will show WBC population dynamics that areunchanged or changed in a qualitatively different manner.

Because serum troponin levels are often normal in patients subsequentlydiagnosed with MI, consideration of WBC population dynamics can helpidentify patients with ACS who have initially negative troponin and willmost likely be found with an elevated troponin in the next severalhours.

As shown herein, patients diagnosed with MI have significantly differentWBC dynamics from those who are healthy, even after controlling forabsolute WBC count. The present methods can help identify patients beingevaluated for MI who are most likely to have an elevated Tn level in thenear future and thus receive that diagnosis.

In addition to providing complementary information about a patient'sclinical state, this model generates novel hypotheses about theunderlying pathophysiological perturbations to WBC population dynamics,which represent the direct pathologic effects of disease, as well as thephysiologic response to this pathology. For instance, the median andvariance of the lymphocyte D_(ALL) and α_(IAS) parameters are higher inthe cohort of patients who go on to have an elevated Tn-T measurement.This finding suggests that the distribution of the volumes ofcirculating lymphocytes widens for patients developing MI. Lymphocytesare hyperproliferative cells that continue to proliferate uponactivation, and this widening of the size distribution could beattributed to the presence of greater numbers of naïve cells, smalleractivated cells entering the circulation from the bone marrow or thymus,or larger activated cells undergoing further proliferation¹⁴⁻¹⁶.Lymphocytes do not generally have a granular and complex cytoplasmicstructure, and the finding of an increase in the measured internalcomplexity of these agranulocytes may reflect activation as consequenceof progressing myocardial ischemia. The ALL measurement generallyreflects cell size, and the significant difference in α_(ALL) shown inFIG. 3A suggests enrichment of smaller neutrophils in advance of aclinical diagnosis of MI, as compared to patients who remain stable.Smaller neutrophils have been shown to be older¹⁷, and this enrichmentmay reflect a consumption of younger neutrophils or a state ofactivation which is associated with a reduction in cell size^(18,19).The modified parameter depicting the lobularity of the neutrophils isconsistent with the presence of an increased number of band neutrophilsin the circulation, as has been shown before^(20,21). The decreasedmonocyte α_(ALL) for patients progressing to MI suggests an enrichmentin smaller monocytes in the circulation, which could be attributed toaccelerated proliferation or maturation²².

Hematologic Malignancy

Subjects with elevated WBC count (e.g., WBC count>11×10³ cells/ul)(“leukocytosis”) are most likely to have an underlying infection(“reactive leukocytosis”) or a hematologic malignancy (“malignantleukocytosis”). Because the treatments for these conditions differgreatly, and early intervention can be crucial to outcome, it isimportant to have a rapid method of making a differential diagnosis. Asdescribed herein, five of twelve of the model parameters were differentwith statistical significance between reactive and malignantleukocytosis, and a cross-validated decision tree classifier using asubset of parameters (α_(SSC,L), α_(SSC,M), α_(RNA/DNA,L), D_(SSC,L),and D_(SSC,M)) could distinguish patients who end up with each diagnosiswith an accuracy of about 82%. Patient CBC measurements were used toestimate the best-fit parameters for each patient using the model andstandard parameter estimation methods. The classifier was then developedusing supervised learning techniques to train a decision tree classifierusing model parameters that were significantly different for thepatients.

A subject diagnosed with an underlying infection can be, e.g., furtherevaluated to determine the site (i.e., location in the body of thesubject) and species of infection and/or treated with an antibioticregimen. A subject diagnosed with a malignancy can be, e.g., furtherevaluated (for instance by serum protein electrophoresis, flow cytometryof peripheral blood, other clinical laboratory assay, bone marrowbiopsy, or imaging) to determine the specific type of malignancy, and/ortreated with standard anti-cancer therapies, e.g., depending on the typeof cancer by purine analogs such as fludarabine, alkylating agents suchas chlorambucil, monoclonal antibodies such as rituximab, tyrosinekinase inhibitors, or other chemotherapy, targeted molecular therapy,and/or radiation. Malignancies that can be first identified this wayinclude ALL, AML, CLL, CML, multiple myeloma, lymphomas, and solidtumors triggering an overt inflammatory response. The model can helpdifferentiate between these diagnoses and can also help identify morebenign or more severe cases of each, for instance FIGS. 11 and 13 showhow more benign and more severe cases of AML and CLL can be identifiedearlier, enabling earlier treatment.

EXAMPLES

The invention is further described in the following examples, which donot limit the scope of the invention described in the claims.

Example 1 White Blood Cell Population Dynamics in Acute CoronarySyndrome

The complete blood count (CBC) is one of the most common clinical tests,integral to the diagnosis, treatment, and monitoring of almost alldiseases because it provides a simple high-level assessment of health ofthe patient's hematologic and immunologic systems by reporting anestimate of the current number of each type of blood cell circulatingper unit volume blood. Increases or decreases in the counts if differentcell types may indicate anemia, infection, malignancy or more. Mostroutine CBCs involve high-resolution and high-throughput single-cellmeasurements of the morphology of tens of thousands of blood cells,providing single-cell details of morphology, protein concentration, orother characteristics. These single-cell characteristics reflect statesof maturation, activation, production, destruction and the perturbationof those processes in different disease conditions. If we can inferthese states and their rates of change from routine blood counts, we candiagnosis disease earlier and more precisely. Here we develop amathematical model of white blood cell population dynamics inspired bycellular mechanisms for this purpose. We first show that this model canbe useful to distinguish healthy individuals from those are not healthy,and we then show how the model can improve the risk-stratification ofpatients being evaluated for acute coronary syndrome. This studydemonstrates how mechanistic modeling of existing clinical data canrealize the vision of precision medicine.

Methods

The following materials and methods were used in the Example below.

Patients and Lab Measurements

We analyzed raw data collected during each patient's first CBCmeasurement. We then inferred WBC population dynamics, parameterized bydrift and diffusion terms for neutrophil, lymphocyte, and monocytepopulations. We defined an elevated Troponin measurement to beindicative of an MI⁸. Patients with MI often have elevations in thecount of WBCs^(10,11), and we therefore controlled for WBC count whencomparing cases and controls. A patient with a normal WBC count may behard to diagnose for the underlying causality of the symptom. This studyspecifically focused on patients who have a normal WBC count, and arethus hard to be screened based on CBC alone. The patient subsets werechosen conservatively and were limited to those with normal WBC count atthe time of the Troponin test. Thus, purely based on the patient's CBC,no distinction could be made pertaining to the underlying causes thattrigger the symptoms.

Patient Blood Sample Collection and Characterization

Patient data was accessed under a research protocol approved by thePartners Healthcare Institutional Review Board. All CBC measurementswere made by an Abbott Cell-DYN Sapphire automated hematology analyzer(Abbott Diagnostics, Santa Clara, Calif.). The analyzer made severaloptical measurements, including Axial Light Loss (ALL) representing cellsize, Intermediate Angle Scatter (IAS) representing cellular complexity,Polarized Side Scatter (PSS) representing nuclear lobularity,Depolarized Side Scatter (DSS) distinguishing granulocytes (neutrophilsand eosinophils), and a fluorescence signal separating nucleated redblood cells, stromal cells and the mononuclear agranulocytes(lymphocytes and monocytes)²³. It was hypothesized that cellular sizeand cytoplasmic complexity would provide useful correlates of cellularmaturation and activation and therefore the analysis focused on the ALLand IAS measurements. Since lymphocytes and monocytes aremorphologically mononuclear, the relevance of nuclear lobularity seemedlimited, and hence the PSS measurement was only studied for neutrophils.

The study group (SG) comprises of 1285 patients who had a Troponin-T orTn-T (Roche Diagnostics, Basel, Switzerland) test ordered at MGH(between June 2012-July 2015). Repeat CBC measurements (after June 2012)were also considered for those patients at the time of a Tn measurement.The healthy cohort, or control group (CG), was obtained from serialmeasurements of healthy patients (141 patients), who had not had anabnormal CBC index over a couple years, and who had not visited thehospital within 250 days, in order to enrich for patients whose onlymedical visits were for annual physical examination.

Upon filtering the overall set of patients (SG), we could identify asubset of interest, ‘Low Tn-T’, containing 91 patients (pairs of bloodsamples, n=153) who have a low Tn-T measurement (Tn-T<=0.03 ng/mL),while the high Tn-T group (Tn-T>=0.09 ng/mL), ‘High Tn-T’, contains 80patients (n=201 separate blood samples). To ensure accurate capture ofthe dynamical behavior of the population, samples not rendering a goodparameter fit (Objective function/sum of square of error, SSE≥0.005 forLymphocyte and Monocytes, SSE≥0.007 for Neutrophils) were excluded. Wefinally end up with 102 unique patients and have ensured that they havea normal WBC count (4,000-11,000 cells/μl) at the first time point, andWBC<17,000 at the time of Tn-T being ordered, and have good parameterfits. These two cohorts were also matched based on their WBC count(difference less than 0.5×10³ cells/μl). FIG. 5A suggests no significantdifference in the WBC differentials between the two cohorts in question,rendering them indistinguishable based on their bulk WBC measurement anddifferential.

A validation set of 100 patients (Validation Group, or VG) wasconsidered to test the accuracy of classification based on modelparameters. Patients who had Tn-T measurements at MGH after August 2015were considered in this cohort. (FIG. 4C-F)

Mathematical Model

The blood count provides a multivariate distribution of single-celloptical scatter properties that relate to single-cell size, cytoplasmicgranularity, nuclear morphology, and other characteristics. Theevolution over time of the probability density (P) of these single-cellproperties was modeled, and this evolutionary process for each cellpopulation was decomposed into drift (α) and diffusion (D) processes.The Fokker-Planck equation is a partial differential equation thatdescribes this sort of temporal evolution of a probability densityfunction under forces of drift and diffusion. The model presented hereinprovides a description of the true WBC population dynamics, withresolution limited by the underlying measurements comprising the CBC.This model utilizes known cellular physiology where possible and makesinformed assumptions otherwise.

The general Fokker-Planck equation describing the time-based evolutionof P under drift (α) and diffusion (D) used was the following:

$\begin{matrix}{\frac{\partial P_{i}}{\partial t} = {{\nabla\left( {P_{i}\alpha} \right)} + {\nabla{.\left( {D.{\nabla P_{i}}} \right)}}}} & (1)\end{matrix}$

In Equation 1. P_(i) is the probability density for the single-cellmeasurements of the i^(th) WBC sub-population (i∈neutrophils,lymphocytes, monocytes). α depicts the “velocity” of the drift term, andD depicts the diffusion coefficient. See FIG. 1 for a schematic of anexemplary modeling approach¹². Using the drift and the diffusion term inthe equation, the trajectory of the heterogeneous cellular populationwas mimicked as it deviated from a healthy state or fluctuated around ahealthy state. The birth and death of cells, or more generally, thefluxes in and out of circulation, were implicitly modeled in the driftterm of the equation. The intent was to model the probability density ofcellular activation, maturation, etc., which can be appropriatelycaptured by the Fokker-Planck equation, while acknowledging thelimitations posed by gaps in physiologic knowledge.

The lineage specific master equation can be written as

$\begin{matrix}{\frac{\partial P_{i}}{\partial t} = {{\frac{\partial}{\partial x_{ALL}}\left( {\alpha_{{ALL},i}P_{i}} \right)} + {\frac{\partial}{\partial x_{IAS}}\left( {\alpha_{{IAS},i}P_{i}} \right)} + {D_{{ALL},i}\frac{\partial^{2}P_{i}}{\partial x_{ALL}^{2}}} + {D_{{IAS},i}\frac{\partial^{2}P_{i}}{\partial x_{IAS}^{2}}}}} & (2)\end{matrix}$

In Equation 2, P_(i) is the 2-D probability density of the i^(th) WBCsubpopulation, D_(ALL,i) and D_(IAS,i) are the diffusive coefficientswith respect to the ALL and the IAS dimensions, and α_(ALL,i), α_(IAS,i)are the drift parameters.

Model Details

The morphology (e.g., size and complexity) of individual cells can beutilized as a crude indicator of cell age and activation state, and thedistribution of these characteristics can be correlated with manydisease processes. There remain unanswered questions regarding thelifecycle of WBCs in general and during heterogeneous pathologicconditions that alter rates of activation, maturation, and apoptosis.Therefore, source terms (e.g. birth and death) were not included inorder to avoid making strong assumptions about the rates of production,proliferation, or turnover. Instead, the drift and diffusion termsprovided an overall lumped quantification of those processes and theireffects on the distribution of cellular characteristics.

The model for the time-based evolution of the distribution of lymphocyteALL and IAS (P_(LYM)) is written in the form of a drift-diffusion orFokker-Planck equation:

$\begin{matrix}{\frac{\partial P_{LYM}}{\partial t} = {{\frac{\partial}{\partial x_{ALL}}\left( {\alpha_{{ALL},L}P_{LYM}} \right)} + {\frac{\partial}{\partial x_{IAS}}\left( {\alpha_{{IAS},L}P_{LYM}} \right)} + {D_{{ALL},L}\frac{\partial^{2}P_{LYM}}{\partial x_{ALL}^{2}}} + {D_{{IAS},L}\frac{\partial^{2}P_{LYM}}{\partial x_{IAS}^{2}}}}} & (3)\end{matrix}$The drift terms (∂/∂x_(ALL) and ∂/∂x_(IAS)) captured the changes in themedian heterogeneity with respect to a morphological attribute, whilethe diffusion terms (∂²/∂x_(ALL) ² and ∂²/∂x_(IAS) ²) tracked thechanges in the variance of the distribution. A change in the centraltendency or median was generally hypothesized to be caused by a changein the distribution of ages or activation states in the circulatingpopulation. In Equation 3, P_(LYM) is the 2-D probability density of thelymphocyte population, D_(ALL,L) and D_(IAS,L) are the diffusivecoefficients with respect to the ALL and the IAS dimensions.

μ_(Pend,IAS) and μ_(Pend,ALL) (see below) represent the median of theIAS and ALL distribution of the final probability density (targetdistribution used for the fitting) and α₁, α₂ are the fitted driftparameters. The drift in terms of the ALL grid (FIG. 5B) is expressed as

$\begin{matrix}{\alpha_{ALL} = {\alpha_{1}\left\{ \begin{matrix}{\frac{x_{ALL}}{\mu_{P_{{end},{ALL}}}},} & {{{when}x_{ALL}} < \mu_{P_{{end},{ALL}}}} \\{\frac{\mu_{P_{{end},{ALL}}}}{x_{ALL}},} & {{{when}x_{ALL}} \geq \mu_{P_{{end},{ALL}}}}\end{matrix} \right.}} & (4)\end{matrix}$

and, the drift with respect to the IAS grid is expressed as

$\begin{matrix}{\alpha_{IAS} = {\alpha_{2}\left\{ \begin{matrix}{{1 - {2\frac{x_{IAS}/\mu_{P_{{end},{IAS}}}}{1 + {x_{IAS}/\mu_{P_{{end},{IAS}}}}}}},} & {{{when}x_{IAS}} < \mu_{P_{{end},{IAS}}}} \\{{2\frac{x_{IAS}/\mu_{P_{{end},{IAS}}}}{1 + {x_{IAS}/\mu_{P_{{end},{IAS}}}}}},} & {{{when}x_{IAS}} \geq \mu_{P_{{end},{IAS}}}}\end{matrix} \right.}} & (5)\end{matrix}$The growth rate of individual lymphocytes as a function of cellular ageor size is unclear and difficult to measure. Some previous investigatorshave found evidence that the growth rate of lymphoblasts is proportionalto volume up to a point and then declines roughly linearly withincreasing size²⁴. ALL dynamics were represented in a qualitativelycompatible way. The growth rate was assumed to increase linearly up tothe median of the final ALL distribution after which it decreases. Thegrowth rate at zero volume is zero, and goes up to a maximum value ofα₁.

It was hypothesized that an important determinant of the cytoplasmiccomplexity and granularity of cells was cellular responses to activationsignals. Therefore, the typical rate of change was modeled as initiallyvery slow and increasing quickly following a signal before stabilizingat a poised level. Michaelis-Menten kinetics are a standard way to modelthis sort of signaling response, as shown in Equation 5.

The population dynamics of neutrophil and monocyte populations weremodeled similarly.

$\begin{matrix}{\frac{\partial P_{MON}}{\partial t} = {{\frac{\partial}{\partial x_{ALL}}\left( {\alpha_{{ALL},M}P_{MON}} \right)} + {\frac{\partial}{\partial x_{IAS}}\left( {\alpha_{{IAS},M}P_{MON}} \right)} + {D_{{ALL},M}\frac{\partial^{2}P_{MON}}{\partial x_{ALL}^{2}}} + {D_{{IAS},M}\frac{\partial^{2}P_{MON}}{\partial x_{IAS}^{2}}}}} & (6)\end{matrix}$ $\begin{matrix}{\frac{\partial P_{NEU}}{\partial t} = {{\frac{\partial}{\partial x_{ALL}}\left( {\alpha_{{ALL},N}P_{NEU}} \right)} + {\frac{\partial}{\partial x_{IAS}}\left( {\alpha_{{IAS},N}P_{NEU}} \right)} + {D_{{ALL},N}\frac{\partial^{2}P_{NEU}}{\partial x_{ALL}^{2}}} + {D_{{IAS},N}\frac{\partial^{2}P_{NEU}}{\partial x_{IAS}^{2}}}}} & (7)\end{matrix}$P_(MON) and P_(NEU) are the 2-D probability distributions of ALL and IASfor the monocyte and neutrophil subpopulations. The drift^(25,26) anddiffusion terms are similar to the lymphocyte model (Equations 4, 5).

Because neutrophils have much more heterogeneous nuclear morphology, amodel for the population dynamics of neutrophil nuclear morphology wasincluded as well. Previous investigators have demonstrated thatneutrophil nuclear morphology is altered in response to disease, inparticular the fraction of neutrophils with band or segmented nucleusmorphology has been shown to increase in states of inflammation such asneonatal sepsis²⁷. The lobularity of the nucleus is reflected in thePolarized Side Scatter (PSS) measurement. The bottom 2.5 percentile ofPSS values for the neutrophils in each sample was calculated todistinguish low lobularity (as seen in band neutrophils) from highlobularity (fully segmented neutrophils). The size of fraction ofneutrophils that have a PSS value lower than this threshold was modeledand was hypothesized to reflect that reflect the fraction of immatureneutrophils in the circulation. This threshold (PSS^(th)=1e4) was chosenas the point depicting the upper quartile of the bounding pointseparating the 2.5^(th) percentile of PSS for neutrophils in allsamples. The fractions are compared at the patient's healthy state(frac₁), versus at the time point of interest (frac₂), and a modifiedparameter is obtained asK _(PSS)=frac₂(frac₂−frac₁)  (8)

The model quantified the deviation from the healthy state for theparticular patient in terms of the fraction of neutrophils withsignificantly reduced lobularity.

Numerical Solution

The Fokker-Planck equation presented in the previous section was solvednumerically using the finite-difference method. Upon discretization ofthe equation in the spatial coordinates, an ordinary differentialequation (ODE) was obtained which can be solved using explicit solutiontechniques. The resulting discretized ODE can be written as

$\begin{matrix}{\frac{{dP}_{{LYM}_{i,j}}}{dt} = {{\alpha_{ALL}\frac{P_{{LYM}_{i,j}} - P_{{LYM}_{{i - 1},j}}}{\Delta x_{ALL}}} + {\alpha_{IAS}\frac{P_{{LYM}_{i,j}} - P_{{LYM}_{i,{j - 1}}}}{\Delta x_{IAS}}} + {D_{ALL}\frac{P_{{LYM}_{{i + 1},j}} - {2P_{{LYM}_{i,j}}} - P_{{LYM}_{{i - 1},j}}}{\Delta x_{ALL}^{2}}} + {D_{IAS}\frac{P_{{LYM}_{i,{j + 1}}} - {2P_{{LYM}_{i,j}}} - P_{{LYM}_{i,{j - 1}}}}{\Delta x_{IAS}^{2}}}}} & (9)\end{matrix}$

For the lymphocytes, the ALL grid was discretized into 40 bins, and theprobability density in the i^(th) ALL bin was described using the firstsubscript in Equation 9. The IAS grid was also discretized into 40 bins,and the probability density in the j^(th) IAS bin was denoted by thesecond subscript. The neutrophil model was solved by discretizing theALL grid into 60 bins, and the IAS grid into 40 bins. Similarly,discretizing the ALL grid into 30 bins, and the IAS grid into 35 binssolved the monocyte model. Discretization strategies were chosen basedon the typical range and variation for these measurements in thedifferent subpopulations. The resulting ODE was solved using thevariable-step, variable-order (VSVO) solver by employing the ode15sfunction within MATLAB 2015b (Mathworks®, Natick, Mass., USA). The ALLand IAS grids are normalized in order to span between 0 and 1. The upperand lower bounds for normalizing the ALL grid were 5×10e2 and 3×10e4,while the bounds for the IAS grid were 5×10e2 and 2.5×10e4 respectively.These bounds were chosen by analyzing the maximum and minimum valuesthat typically occur in the WBC measurements (across all the datasets).The model was solved for an arbitrary time point (t=0.5) for all theblood samples in order to normalize parameters as a function of spatialand time coordinates.

Parameter Estimation

The Fokker-Planck equation (Equation 2) was solved iteratively to obtainoptimal parameters that started with the initial measured cellulardistribution for the patient and evolve according to the equation tomatch the final measured distribution of the cellular population. Theend point reached according to Equation 2 was compared with thepatient's actual measured distribution, and the difference wasminimized. The error, or objective function (Obj), is defined asfollows:

$\begin{matrix}{{Obj} = {\sum\limits_{i}{\sum\limits_{j}\left( {P_{{LYM}_{i,{j - t_{end}}}} - P_{{LYM}_{i,j,{oncasure}}}} \right)^{2}}}} & (10)\end{matrix}$

The optimization problem was solved using the Nelder-Mead simplex method(fminsearch using MATLAB), followed by employing the gradient-basedLevenberg-Marquardt equation (fminunc using MATLAB). In order to ensurethe robustness of the optimization results, 10 different starting pointsfor the optimization were picked in parameter space using theLatin-Hypercube sampling method. The final accepted parameter set wasselected from the list of ten optimization results (using the differentstarting points) based on both the objective function (smallest value)and the first order optimality condition from the gradient-basedoptimization algorithm (smallest value).

Assessing the Robustness of this Framework:

The expression describing the drift relative to the ALL grid shown inEquation 4 was developed to be consistent with what is known about thebiological processes of cellular production, maturation, activation andclearance. Given the substantial uncertainty in the details of theseprocesses, the precise expression in Equation 4 is an estimate of thetrue biological process. The precise mathematical form of thatexpression is not important, but the qualitative biological features itrepresents are. In order to increase confidence that the resultsdepended on these qualitative features and not the precise and arbitraryfunctional forms, alternative expressions were developed that differedin their mathematical form but retained consistency with the qualitativebasis. The drift in the ALL dimension can alternatively be quantifiedlike the following:

$\begin{matrix}{\alpha_{ALL}^{\prime} = {\alpha_{1}^{\prime}\left\{ {\begin{matrix}{\left( \frac{x_{ALL}}{\mu_{P_{{end},{ALL}}}} \right)^{2},} & {{{when}x_{ALL}} < \mu_{P_{{end},{ALL}}}} \\{\left( \frac{x_{ALL} - \mu_{P_{{end},{ALL}}}}{\mu_{P_{{end},{ALL}}}} \right)^{2},} & {{{when}x_{ALL}} \geq \mu_{P_{{end},{ALL}}}}\end{matrix}{or}} \right.}} & (11)\end{matrix}$ $\begin{matrix}{\alpha_{ALL}^{''} = {\alpha_{1}^{''}\left\{ \begin{matrix}{\frac{x_{ALL}}{\mu_{P_{{end},{ALL}}}},} & {{{when}x_{ALL}} < \mu_{P_{{end},{ALL}}}} \\{\frac{x_{ALL} - \mu_{P_{{end},{ALL}}}}{\mu_{P_{{end},{ALL}}}},} & {{{when}x_{ALL}} \geq \mu_{P_{{end},{ALL}}}}\end{matrix} \right.}} & (12)\end{matrix}$

Alternate expressions have also been considered for the IAS drift term:

$\begin{matrix}{\alpha_{IAS}^{\prime} = {\alpha_{2}^{\prime}\left\{ \begin{matrix}{{\min\left( {1,{\max\left( {0,\frac{x_{IAS} - \mu_{P_{{end},{IAS}}}}{\mu_{P_{{end},{IAS}}}}} \right)}} \right)},} & {{{when}x_{IAS}} > \mu_{P_{{end},{IAS}}}} \\{{\min\left( {1,{\max\left( {0,\frac{\mu_{P_{{end},{IAS}}} - x_{IAS}}{\mu_{P_{{end},{IAS}}}}} \right)}} \right)},} & {{{when}x_{IAS}} \geq \mu_{P_{{end},{IAS}}}}\end{matrix} \right.}} & (13)\end{matrix}$FIGS. 8A-H confirm the robustness of the model to variation in theprecise mathematical details while retaining qualitative consistencywith the coarsely defined biological mechanisms. Different expressionsfor the drift term did not provide significantly different parameters,and did not alter the results.

Comparing parameter values for patients who did not have any cardiacsymptoms (lack of a Tn-T measurement is assumed to be associated with ahealthy state of the patient, provided none of the CBC parameters areabnormal as well), potential cardiac symptoms but not acute myocardialinfarction or AMI (low Tn-T), and cardiac discomfort caused by AMI (highTn-T) also yields statistically significant differences, as shown inFIG. 9A-L.

Results

The effect of an acute disease process on WBC population dynamics wasassessed by comparing model parameters for healthy individuals toparameters for patients with elevated troponin levels, the gold standardmarker for MI¹³. The absolute WBC count is a well-established marker ofdisease in general and MI in particular, and in order to assess theeffect of myocardial ischemia and infarction on WBC population dynamicsindependent of changes in WBC count, cases and were matched to controlsto ensure that each case-control pair differed in total WBC count byless than 0.5×10³ cells/μl at the time of each CBC used to inferpopulation dynamics. The CBC pairs for each case and control were thusindistinguishable based on the WBC count, but FIGS. 2A-E show that 6 of13 model parameters differed between the two groups with statisticalsignificance.

This clear difference in dynamic model parameters shows that MIsignificantly perturbs WBC population dynamics independent of WBC countand that this perturbation was detectable even with this coarse model ofWBC population dynamics based on routinely available CBC raw data. Seeequations 3, 6, and 7 for more detail. The diffusion coefficient in ALL(or size) was significantly different for all three WBC subtypes,indicating a difference in the composition of the cellular sizes for thecase versus control. In addition to that, all the parameters weresignificantly different (between the cases and controls) for themonocyte population. This comparison comprised healthy (“Control”)patients versus patients visiting the hospital with symptoms indicatingchest discomfort, however not everyone in the “Study” group had AMI, butall were acutely ill.

It was hypothesized that WBC population dynamics would reflect some ofthe earliest effects and responses to the myocardial ischemia precedingMI. At the time of symptom presentation for the Study patients in FIGS.2A-E, these pathologic effects and physiologic responses were wellunderway and, even after matching patients for absolute WBC counts,clearly distinguished the typical patient with MI from that without.Assuming that these perturbations to WBC population dynamics occur veryearly, this model can be used to identify some of the patients with MIbefore the myocardial ischemia has progressed to the point wheresignificant myocardial cell death has occurred, with subsequent leakageof Tn into the bloodstream. This hypothesis was tested by comparing WBCpopulation dynamics for patients at the time of an initially negativeTn, some of whom maintained a stably negative Tn, and others whoprogressed to an elevated Tn and a diagnosis of MI. Again, patients werematched by absolute WBC count to focus on differences in WBC dynamicsthat are independent of WBC count. FIGS. 3A-F show that 5 of 13parameters were different between these two groups with statisticalsignificance.

The parameters distinguishing the two groups with statisticalsignificance were lymphocyte D_(ALL), α_(IAS); neutrophil α_(ALL),K_(PSS); and monocyte D_(ALL). The patients whose Tn-T went upeventually (indicating AMI), had a higher D_(ALL) suggesting a widersize distribution. The drift with respect to IAS was increased in thehigh Tn cohort, suggesting a higher fraction of cells with greaterinternal complexity. α_(ALL) was reduced in neutrophils, suggestingsmaller cells. Earlier identification of patients whose Tn is likely tobecome elevated would enable earlier intervention and possibly improvedoutcomes for these patients. To assess the utility of this approach forassisting in the risk-stratification of ACS patients, a five-foldcross-validated decision tree classifier was built with the significantmodel parameters (lymphocyte D_(ALL), α_(IAS); neutrophil α_(ALL) andK_(PSS); and monocyte α_(ALL) and D_(IAS)) and the data from thepatients shown in FIGS. 3A-F (training set). An independent set ofpatients with negative Tn levels was then identified, and the accuracyof the classifier assessed when predicting which of those patients wouldeventually have an elevated Tn level in the subsequent 48 hours. FIGS.4A-D show the receiver operating characteristic (ROC) curves andconfusion matrices for the training set and validation sets. Theclassifier was developed with a training set, and the classifier thusprovided a similar AUC for both data sets as expected whencross-validation was used.

Example 2 White Blood Cell Population Dynamics in Reactive and MalignantLeukocytosis

The present methods were also used to distinguish subjects with reactiveversus malignant leukocytosis. A retrospective study was performed onsamples from 250 leukemia cases and about 350 non-leukemia cases.

Reactive leukocytosis cases were defined based upon a CBC with all ofthe following criteria: CBC showed an elevated WBC count (>11e3/ul) but<20e3/ul; the patient had no elevated WBC counts in 12 months prior toCBC; the patient had a positive culture (blood, urine, or sputum) within+/−7 days from the CBC; the patient had no cancer diagnosis in the 6months following the CBC.

Malignant leukocytosis cases were defined based on CBC all of thefollowing criteria: CBC showed an elevated WBC count but <20e3 ul; thepatient had no elevated WBC counts in the 12 months prior to CBC; thepatient had NO positive culture (blood, urine, or sputum) within +/−30days from the CBC; the patient had a new diagnosis of ALL, AML, CML, orCLL in the 6 months following the CBC. These measurements were performedusing the Sysmex XE-5000 instrument, which utilizes the opticalmeasurements defined by the side scatter and the RNA/DNA fluorescencestain to categorize the various cellular subtypes in the WBC population.We assume that the nuclear size depicted by the RNA/DNA information issimilar to the cellular size, owing to the large nucleus and almostabsent cytoplasmic space characteristic of lymphocytes

As above, a Fokker-Planck based phenomenological model was used for eachlineage:

${\frac{\partial P_{LYM}}{\partial t} = {{\frac{\partial}{\partial x_{SSC}}\left( {\alpha_{{SSC},L}P_{LYM}} \right)} + {\frac{\partial}{\partial x_{{DNA}/{RNA}}}\left( {\alpha_{{{DNA}/{RNA}},L}P_{LYM}} \right)} + {D_{{SSC},L}\frac{\partial^{2}P_{LYM}}{\partial x_{SSC}^{2}}} + {D_{{{DNA}/{RNA}},L}\frac{\partial^{2}P_{LYM}}{\partial x_{{DNA}/{RNA}}^{2}}}}},$$\alpha_{{SSC},L} = {\alpha_{2,L}\left\{ {\begin{matrix}{{1 - {2\frac{\frac{x_{SSC}}{\mu_{P_{{end},{SSC},L}}}}{1 + \frac{x_{SSC}}{\mu_{P_{{end},{SSC},L}}}}}},} & {{{when}x_{SSC}} < \mu_{P_{{end},{SSC},L}}} \\{{2\frac{\frac{x_{SSC} - \mu_{P_{{end},{SSC},L}}}{\mu_{P_{{end},{SSC},L}}}}{1 + \frac{x_{SSC} - \mu_{P_{{end},{SSC},L}}}{\mu_{P_{{end},{SSC},L}}}}},} & {{{when}x_{SSC}} \geq \mu_{P_{{end},{SSC},L}}}\end{matrix},{and}} \right.}$$\alpha_{{{RNA}/{DNA}},L} = {\alpha_{1,L}\left\{ {\begin{matrix}{\frac{x_{{RNA}/{DNA}}}{\mu_{P_{{end},{{RNA}/{DNA}},L}}},} & {{{when}x_{{RNA}/{DNA}}} < \mu_{P_{{end},{{RNA}/{DNA}},L}}} \\{{2\frac{\mu_{P_{{end},{{RNA}/{DNA}},L}}}{x_{{RNA}/{DNA}}}},} & {{{when}x_{{RNA}/{DNA}}} \geq \mu_{P_{{end},{{RNA}/{DNA}},L}}}\end{matrix}.} \right.}$

The distribution for lymphocyte morphological attributes at an earliertime point measurement for the patient was considered as initialconditions of the PDE. Following the trajectory described in the PDE,the distribution was fit at the later time point to obtain “optimal”parameters.

As shown in FIGS. 10A-L, Kruskal-Wallis tests confirm significantlydifferent parameters for the two cohorts, which can then be utilized todevelop a multivariate classifier with additional patient data. Across-validated decision tree classifier was developed with four-foldcross-validation and had an overall accuracy of about 82%.Discrimination efficiency can be improved when (i) the model structureis optimized for use with the Sysmex optical data, and (ii) amultivariate discriminant is carefully developed.

Example 3 Exemplary Diagnostic Scenarios

The following provide exemplary diagnostic scenarios using methodsdescribed herein.

(1) An apparently healthy patient at an outpatient visit has a WBC countof 8. WBC population dynamics modeling shows the estimated neutrophilbirth rate is abnormally high, suggesting an acute subclinical infectionor other process. The patient can be scheduled for a more detailedfocused physical exam in the short term, or a urine culture, sputumculture, or throat swab can be performed in the near term.

(2) A patient hospitalized for exacerbation of congestive heart failurehas been stabilized and is preparing for discharge. WBC populationdynamics modeling shows an abnormally high lymphocyte birth ratesuggesting an acute subclinical infection that greatly increases thatpatient's chances of being rehospitalized after discharge. The patient'sdischarge can be delayed by 24 hours for extra monitoring.

(3) A patient with a low platelet count can undergo modeling of plateletpopulation dynamics to help distinguish between consumptive andproductive causes or response to treatment.

REFERENCES

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OTHER EMBODIMENTS

It is to be understood that while the invention has been described inconjunction with the detailed description thereof, the foregoingdescription is intended to illustrate and not limit the scope of theinvention, which is defined by the scope of the appended claims. Otheraspects, advantages, and modifications are within the scope of thefollowing claims.

What is claimed is:
 1. A system comprising a processing device, and oneor more computer-readable non-transitory media storing instructions thatare executable by the processing device, and upon execution cause theprocessing device to perform operations comprising: estimating a valueof a parameter indicative of white blood cell (WBC) population dynamicsof a patient based on data indicative of a property value of each WBC ina sample of white blood cells (WBCs) of the patient, the property valueof a WBC being indicative of an age of the WBC; and providinginformation for treatment or diagnosis of a condition of the patientassociated with an inflammatory or immune system response based on theparameter.
 2. The system of claim 1, wherein the WBCs comprise cellsselected from the group consisting of neutrophils, lymphocytes, andmonocytes.
 3. The system of claim 1, wherein the operations furthercomprise receiving data indicative of a complete blood count of thepatient, the data indicative of the complete blood count beingindicative of the property value of each WBC.
 4. The system of claim 1,wherein the property value of the parameter is estimated based on dataindicative of a predefined normalized property value of WBCs.
 5. Thesystem of claim 1, wherein the operations further comprise: receivingdata indicative of a first complete blood count of the patient in whichthe property value of each WBC in a first sample of WBCs is measured,and receiving data indicative of a second complete blood count of thepatient in which the property value of each WBC in a second sample ofWBCs is measured, wherein the value of the parameter is estimated basedon the data indicative of the first complete blood count and the dataindicative of the second complete blood count.
 6. The system of claim 1,wherein the operations further comprise: receiving data indicative of anormal template or ensemble of normal complete blood counts in which theproperty value of each WBC in a first sample of WBCs is measured, andreceiving data indicative of a second complete blood count of thepatient in which the property value of each WBC in a second sample ofWBCs is measured, wherein the value of the parameter is estimated basedon the data indicative of the normal template or ensemble of normalcomplete blood counts and the data indicative of the second completeblood count.
 7. The system of claim 1, wherein the property value isindicative of a property of each WBC selected from the group consistingof cell size, cytoplasmic granularity, morphology, nuclear morphology,and nuclear granularity.
 8. The system of claim 1, wherein receiving thedata indicative of the property value of each WBC comprises receivingdata indicative of axial light loss measurements of the sample of WBCs,intermediate light loss measurements of the sample of WBCs, or polarizedside scatter measurements of the sample of WBCs.
 9. The system of claim1, wherein the parameter indicative of the WBC population dynamics ofthe patient is indicative of a drift or a diffusion of the WBCpopulation dynamics.
 10. The system of claim 9, wherein the parameter isselected from the group consisting of α_(ALL), D_(ALL), α_(IAS),D_(IAS), K_(PSS), α_(SSC,L), α_(SSC,M), α_(RNA/DNA,L), D_(SSC,L),D_(SSC,M), and D_(RBA/DNA,L).
 11. The system of claim 1, wherein thecondition is selected from the group consisting of a hematologicalmalignancy, acute coronary syndrome, urinary tract infection, and anautoimmune disease.
 12. The system of claim 1, wherein providinginformation for treatment or diagnosis of a condition of the patientassociated with an inflammatory immune system response based on theparameter comprises providing information for treatment or differentialdiagnosis of reactive leukocytosis and malignant leukocytosis.
 13. Thesystem of claim 1, wherein a troponin level of the patient is within thenormal range, and or a WBC count is within normal range.
 14. The systemof claim 1, wherein the data comprises optical, fluorescence, orimpedance single-cell measurements from a complete blood count.
 15. Thesystem of claim 1, wherein the data is indicative of a morphologicalproperty or intracellular composition of each WBC in the sample.
 16. Thesystem of claim 15, wherein the data is indicative of cell size,internal complexity, nuclear lobularity, peroxidase content, or DNA/RNAcontent of each WBC in the sample.
 17. The system of claim 1, whereinthe data comprise one or more of Axial Light Loss (ALL) representingcell size; Intermediate Angle Scatter (IAS) representing cellularcomplexity; Polarized Side Scatter (PSS) representing nuclearlobularity; Depolarized Side Scatter (DSS) distinguishing granulocytes(neutrophils and eosinophils); and a fluorescence signal separatingnucleated red blood cells, stromal cells and the mononuclearagranulocytes (lymphocytes and monocytes).
 18. The system of claim 17,further comprising comparing the one or more values to a referencevalue.
 19. The system of claim 18, wherein the reference valuerepresents an identified cohort of subjects, or a value determined at anearlier or later point in time in the same subject.
 20. A methodcomprising: estimating a value of a parameter indicative of white bloodcell (WBC) population dynamics of a patient based on data indicative ofa property value of each WBC in a sample of white blood cells (WBCs) ofthe patient, the property value of a WBC being indicative of an age ofthe WBC; and providing information for treatment or diagnosis of acondition of the patient associated with an inflammatory or immunesystem response based on the parameter.